Matematik Öğretmeni Adaylarının Pergel-Cetvel ve Dinamik Geometri Yazılımı Kullanarak Yaptıkları Geometrik İnşalar

Abstract

This study aimed to investigate prospective middle school mathematics teachers' geometric constructions and justifications to verify their constructions when they used compass-straightedge. In addition, it was examined that what prospective teachers noticed about geometric constructions in a classroom discussion where dynamic mathematics software (GeoGebra) was used. A total of 68 prospective teachers from middle school mathematics teacher education program participated to the study. Data were obtained by qualitative research ways such as written papers, reflective notes, and classroom discussions. The data were analyzed based on content analysis. The results showed that prospective teachers used four different methods in appropriate parallelism constructions such as perpendicular lines, angle copying, equilateral triangles and rhombus methods. Another important result was that more than half of the prospective teachers did not achieve the appropriate geometric constructions because they made incorrect assumptions in the geometric constructions. Finally, prospective teachers noticed following issues in GeoGebra-supported classroom discussions: (a) alternative construction methods, (b) the necessity of providing solid foundations, (c) the effect of incorrect assumptions in geometric constructions and (d) different roles of dynamic geometry software and compass-straightedge in the process of geometric constructions and justifications.